The skew energy of random oriented graphs

Given a graph G, let Gσ be an oriented graph of G with the orientation σ and skew-adjacency matrix S(Gσ). The skew energy of the oriented graph Gσ, denoted by ES(Gσ), is defined as the sum of the absolute values of all the eigenvalues of S(Gσ). In this paper, we study the skew energy of random oriented graphs and formulate an exact estimate of the skew energy for almost all oriented graphs by generalizing Wigner’s semicircle law. Moreover, we consider the skew energy of random regular oriented graphs , and get an exact estimate of the skew energy for almost all regular oriented graphs.